What is the derivative of ##y=ln(1/x)##?
February 20th, 2023
##y’=-1/x##
Full solution
##y=ln(1/x)##
This can be solved in two different ways,
Explanation (I)
The simplest one is, using logarithm identity,
##log(1/x^y)=log(x^-y)=-ylog (x)##, similarly following for problem,
##y=-ln(x)##
##y’=-(ln(x))’##
##y’=-1/x##
Explanation (II)
Using ,
##y’=(ln(1/x))’##
##y’=1/(1/x)*(-1/x^2)=-1/x##
##y’=-1/x##